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Yang Yang

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Open access Jul 2026

Assessing Constrained Nuclear–Electronic Orbital Theory for the Floppy CH 5 + Ion: Geometry-Dependent Zero-Point Effects on Structure, Hydrogen Rearrangement Dynamics, and Simulated IR Spectra

Recently, constrained nuclear–electronic orbital (CNEO) theory has been developed to incorporate nuclear quantum delocalization and zero-point effects into quantum chemistry calculations and ab initio molecular simulations. Motivated by discussions with John Stanton, we apply CNEO methods to protonated methane, CH5 +, as a stringent test case for the quantum-corrected effective-potential framework. CH5 + is a prototypical penta-coordinated nonclassical carbonium ion with a highly anharmonic potential energy surface, many low-lying geometries connected by low barriers, and extensive fluxional motion. Using CNEO, we examine the effective structural features, hydrogen rearrangement dynamics, and simulated IR spectra of CH5 +. The CNEO effective potential energy surface exhibits a minimum with C2v symmetry, which is more symmetric than the minimum-energy eclipsed-Cs structure on the conventional potential energy surface. CNEO molecular dynamics predicts more frequent hydrogen rearrangement than conventional ab initio molecular dynamics, with pronounced rearrangement observed starting from 50 K. A Fourier-filtered analysis of C–H bond-length distributions along the trajectories, combined with a Gaussian mixture model, reveals three structural and dynamical motifs: equilibrium-like, fluxional, and transition-state hovering configurations. The simulated IR spectra, which are obtained from either harmonic analysis or classical dynamics on the CNEO surface, are compared qualitatively with experimentally observed spectral features. Overall, this work assesses how the computationally efficient CNEO framework captures qualitative structural, dynamical, and spectroscopic trends in the highly fluxional CH5 +, while also highlighting the challenges and shortcomings of this classical-trajectory-based method in a system where fully quantum nuclear effects beyond zero-point effects are important.

Yiwen Wang, Zehua Chen, Yuzhe Zhang et al. · 0 citations
Review Jul 2026

CP2K: An electronic structure and molecular dynamics software package - Dynamics, Transport, and Spectroscopic Response

One of the distinguishing aspects of CP2K is its seamless integration of diverse structural and transition-state optimization techniques with advanced sampling approaches including Monte Carlo, molecular dynamics, and metadynamics, enabling the efficient exploration of complex potential- and free-energy landscapes, including rare events. These capabilities are combined with a broad hierarchy of energy and force evaluation methods, ranging from classical and machine-learned interaction potentials and mixed quantum-classical multiscale and semiempirical schemes, to highly accurate quantum-mechanical electronic-structure approaches. At the heart of the latter lies the Gaussian and plane-wave framework, along with its augmented all-electron generalization, which have been described in detail in our previous code review [T. D. K\"uhne et al., J. Chem. Phys. 152, 194103 (2020)]. Building on this foundation, the present work revisits the methods within CP2K that turn electronic structure into dynamics, transport, and spectroscopic response. Particular emphasis is placed on the coupling between static response calculations and nuclear motion: spectra may be evaluated at optimized structures, averaged over thermally sampled configurations, obtained from time-correlation functions along ab-initio or path integral molecular trajectories, or followed in real time together with electronic and nuclear dynamics. The same modular structure also enables equilibrium and biased transport simulations, from Kubo-type linear response to open-boundary approaches under external potentials, highlighting CP2K's unique capability to unify quantum chemistry with quantum and statistical mechanics within a versatile, holistic simulation environment.

Jan Wilhelm, Anna-Sophia Hehn, Hossam Elgabarty et al. · 1 citation · ⚡1